@VirginiaApplejack based on those 2 anime I think you would like Monster it is a really great anime with mystery, suspense, & delves in the human condition like Death Note. You may also enjoy these if you have not seen them already. Gantz is SciFi based. Elfien Lied another great anime. Ghost in the Shell most likely you have seen this since it is pretty main stream but a great show I recommend the movies and the TV series. And you might like Higurashi no Naku Koro ni (When they Cry) its a bit unique but a great watch if you want your brain messed with.

Both feature length animation rather than comics etc ... for deep meaning and artistry one I saw quite a few years ago now, about a nation's first astronaut I think...can't remember the title. For fun and quirkyness probably Dominion Tank Police.

@Zuffy The only anime I can think of right now that fits that description is The Wings of Honneamise. Its an older anime released back in the mid 80's I think. I tend to lean towards old school anime. I also remember Domionion Tank Police that was a great anime I have it on VHS tape somewhere its been a long time since I've watched it as well.

I've not watched all that much Anime, but apart from the obvious (Studio Ghibli's ouvre), I quite enjoyed Neon Genesis Evangelion in the 90s, and Full Metal Alchemist was quite good too (haven't seen FMA: Brotherhood though).

Currently I was recommended Overlord, which has just started. Not too bad so far.

I recently watched Moribito the Spirit Guardian on Netflix, and was impressed by the series. It's a relatively low-key setting, compared to Dragonball Z, Attack On Titan, or many other anime, which often lean toward a more over-the-top world and action style. I liked the feudal setting of Moribito combined with the role of the main character, who's a female bodyguard of extremely high competence and real depth. Much more interesting for me than a hypersexualized Lolita character surrounded by intensely awkward boys and men who suffer inexplicable nosebleeds (how did that become such a widespread motif?) whenever she jiggles. The story is well developed, based off of what is evidently a hugely successful series of Japanese novels.

As far as anime goes, Samurai Champloo is one of my favourites- love the hip hop style mixed with Edo-era Japan. Not the best overarching story, but great episodic entertainment. I can only speak to season one, but Psycho-Pass was really good. Very fast paced, interesting future dystopia, solid story, and good music...I started it on a whim after seeing it on Netflix, and I can definitely recommend it! Film wise, there's the obvious Studio Ghibli collection. Watched Summer Wars not too long ago and enjoyed it.

For manga, Death Note is probably my favourite. Fullmetal Alchemist, Eyeshield 21, Yu Yu Hakusho, One Piece...lots of the classics! Used to subscribe to the monthly Shonen Jump back in the day, it was always awesome getting it in the mail!

@Molokov Yeah there is so many good staple anime out there EVA is definitely one of them. I remember watching it when it first aired waiting for the next episode to come out then binge watching them all again after they were all released.

@Farlander Moribito is an mazing anime the background art work and animation is gorgeous. The blacksmith scene is one of my all time favorite scenes in an anime. Such a powerful show with an amazing story.

@flabbiercheese As manga goes Death Note & One Piece are extremely popular. I personally prefer the Death Note Manga over the anime. One Piece is just a Juggernaut and insanely entertaining I really need to get back into it I stopped reading it around chapter 650 I think.

Ah, I see, so my confusion probably arises from seeing some anime that's based on manga and seeing the word "manga" in the opening credits; probably.

So, I remembered that I recently-ish watched "Appleseed Alpha," it's computer animated, so does it fall under the umbrella of anime? To keep a little more on topic, if it is classed as anime, then it's probably one of my favourite, apart from (some of) the female characters, they seemed a little, er, lampstand-esque. :/

I do wish I could remember the names of more anime, most of them I saw a long time ago and can only vaguely remember them.

@Zuffy Yeah basically what @farlander said. Appleseed Alpha would fall under the anime category. To make it more confusing Appleseed Alpha is actually based off a manga and is a remake of an anime that came out in the 80's. The 80's/90's I think was the "golden age" of anime a lot of great shows came out then.

Oh gosh, such a broad topic. Well hey, at least I can throw some things in there. Going from the things I have listed in my MAL account, I'll have to break that into top 5 for both, haha, though now that I think of it, some things definitely deserve to be on the list more than others.

Let's go with anime first! -- In no particular order, Samurai Champloo, Princess Mononoke, Clannad After Story, Psycho Pass, and the 2011 version of Hunter X Hunter. The manga one is more consistent with what I remember, so that'll be a bit easier. Again, no real order. Hitman Reborn!, One Piece, Fullmetal Alchemist, Air Gear, and MAR. Phew, lots of good times here.

Generally my tastes are anything cheerful. I love Tsuritama because it is mostly about childhood, being happy, and fishing and platonic love but not romantic love. No fighting or monster of the week stuff, just growing up and taking care of your family during an alien invasion that actually has been predicted hundreds of years ago.